*Only Gargos can actually Kill Tusk
This is the direct quote from the developer’s post. It clearly states that Gargos is the only one that can kill Tusk, and according to Tusk’s story, he’d need Tusk’s sword to do it.
Additionally, he totally does have regeneration. In the dossiers, after Tusk was attacked by Shadow Jago (who failed to kill him) Hisako took him to a cave so he could do just that.
Dossier VII: Two years ago Tusk was blindsided by one of Gargos’ newest creations - the sinister warrior known as Shadow Jago - who attacked Tusk with an Astral relic: The Oblivion Shard. Unable to kill Tusk, Shadow Jago erased the Immortal’s memories. The swordsman collapsed and fell into a coma, but he was discovered on the snowy plains by the last Astral Gatekeeper who brought him to an ice cave (along with his sword Warg-gram), sealing Tusk inside, and leaving him to regenerate.
The only one who can kill Tusk is Gargos. Otherwise he will just come back, as he’s already demonstrated.